Soft bit Viterbi equalizer using partially collapsed metrics

ABSTRACT

First and second partially collapsed metric values are determined for each bit in a symbol transition. Each first partially collapsed metric value is a cumulative metric of starting in a first state and ending in a second state in L transitions with the respective bit in the symbol transition being a first value. Each second partially collapsed metric value is a cumulative metric of starting in the first state and ending in the second state in L transitions with the respective bit in the symbol transition being a second value, the second value differing from the first value. For each bit in the symbol transition, a relative likelihood value is determined based on its respective first and second partially collapsed metric values. A symbol is decoded based on a hard decision performed using the relative likelihood value for each bit in the symbol transition.

FIELD OF THE DISCLOSURE

The present disclosure relates to Viterbi equalizers.

BACKGROUND

A fundamental challenge in wireless communication is the unreliable andhostile nature of wireless channels. A problematic wireless channeldistorts and corrupts a transmitted signal to such a degree that it ismay be virtually unrecognizable at a receiver. This is especially truewhen a line of sight (LOS) condition is not achieved and the signalreaches the receiver after multiple reflections and scatterings. Thedispersive nature of the wireless channel also creates inter-symbolinterference (ISI), which cannot be mitigated by changing RF systemparameters such as frequency plan, transmit power and antenna pattern.

ISI occurs in an 8-PSK (8-state Phase Shift Keying) mode of EDGE(Enhanced Data for GSM Evolution) not only due to the dispersive natureof the channel, but also due to a transmit filter. An EDGE transmitfilter restricts a signal's bandwidth to approximately 200 kHz to ensurecompatibility with a spectral mask previously defined for GMSK (GaussianMinimum Shift Keying) transmission. An ISI-free Nyquist filter in thecase of EDGE would lead to a signal with a 271 kHz bandwidthcommensurate with the symbol rate of EDGE/GSM (Global System for Mobilecommunication). However, since the 8-PSK transmission is restrained tothe 200 kHz bandwidth, Nyquist's ISI free sampling criteria is violated.This results in a transmission with ISI even in a non-dispersive channelwhen LOS is achieved.

The ISI contained within the corrupted signal can be partially mitigatedby passing the signal through an equalizer such as a Linear Equalizer ora Decision Feedback Equalizer (DFE). However, neither the linearequalizer nor the DFE are optimal in terms of minimizing the symbolerror rate.

A non-linear equalizer such as a Maximum Likelihood Sequence Estimator(MLSE) based on the Viterbi Algorithm (VA) is considered to be optimal,and results in the smallest error rate for a linear dispersive channel,such as the wireless channel, or a channel associated with atwisted-pair copper wire. A drawback of the MLSE is the complexity ofthe VA, which increases exponentially with the equalization depth andthe constellation size of the modulation. In the case of a typical urbanenvironment, the dispersive nature of the channel requires anequalization over 3 to 4 symbols which corresponds to a delay spread of11 to 14 seconds. The number of states associated with the VA in theMLSE is 8 to 16 states for GMSK modulation and 512 to 4096 states for8-PSK modulation. The sheer large number of states required in the caseof 8-PSK modulation makes the use of MLSE computationally difficult orprohibitive.

Alternative equalizer structures such as Delayed Decision FeedbackSequence Estimator (DDFSE) and Reduced State Sequence Estimator (RSSE)have been shown to have near optimal performance with a manageable levelof complexity. In the case of DDFSE, a tradeoff between complexity andperformance can be achieved by truncating the depth of equalization withdecision feedback ISI cancellation. RSSE allows for an even finertradeoff between the complexity and performance by using setpartitioning in which one or more modulation symbols are mapped onto apartition. It has been shown that both DDFSE and RSSE can achieve areasonably close performance (e.g. 0.5 to 1.0 dB) in terms of Bit ErrorRate (BER) when compared to the optimum MLSE equalizer.

To improve the performance of the forward error correction (FEC) at thereceiver, soft likelihood values are provided to the decoder instead ofhard bit decisions. The bit-wise soft log-likelihood value is definedas: $\begin{matrix}{L = {\log_{10}\left\lbrack \frac{\Pr\left\{ {b = {+ 1}} \right\}}{\quad{\Pr\left\{ {b = {- 1}} \right\}}} \right\rbrack}} & (1)\end{matrix}$where Pr{b=+1} is the probability of a bit being equal to +1, andPr{b=−1} is the probability of a bit being equal to −1. Although thegeneration of likelihood values requires extra computational complexity,the performance benefits in terms of frame error rate (FER) or blockerror rate (BLER) are considerable. Unlike hard decisions, which arederived from a trellis with a minimum metric, soft likelihood estimationrequires a comparison of the trellis with minimum metric to othertrellises with larger metrics. Optimum soft likelihood information isproduced by symbol-by-symbol, maximum a-posteriori (MAP) decodingalgorithms. However, less computationally intensive algorithms such asSoft Output Viterbi Algorithm (SOVA) are used more commonly for MLSEequalizers.

A challenge in the implementation of RSSE-based equalizers is thegeneration of the soft likelihood values. In a RSSE, some of thenon-surviving trellises required for the calculation of the softlikelihood value are missing. This poses a hurdle for implementing aRRSE equalizer for EDGE systems with an acceptable degree ofperformance. In a recent study, an RSSE-based equalizer for EDGE wasproposed with soft symbol and soft bit estimation based on partialre-growing of the trellises. This algorithm looks at the existence ofthe non-detected path metric for a given bit value, if the non-detectedpath is missing. The missing branch metric and thus the correspondingpath metric are calculated from a state history. The re-growing processadds computational complexity but the overall complexity of thealgorithm is far less than for MLSE.

Existing RSSEs have a soft decision performance that is relativelypoorer than their hard decision performance. This effect becomes moreprominent as the modulation alphabet size increases or as the number ofstates in the equalizer decreases.

BRIEF DESCRIPTION OF THE DRAWINGS

The present invention is pointed out with particularity in the appendedclaims. However, other features are described in the following detaileddescription in conjunction with the accompanying drawings in which:

FIG. 1 is a block diagram of a baseband equivalent model of an EDGEtelecommunication system;

FIG. 2 is a diagram of an embodiment of a mapping of a coded andinterleaved sequence to an 8-PSK constellation;

FIG. 3 is a flow chart of an embodiment of a method to calculate thesoft likelihood values;

FIG. 4 illustrates graphs of a simulated channel bit error rate of a4-state RSSE and a 512 state MLSE for 8-PSK modulation; and

FIG. 5 illustrates graphs of simulated block error rate performance of asoft bit Viterbi equalizer (SBVE) and a soft symbol decision RSSE.

DETAILED DESCRIPTION OF THE DRAWINGS

Disclosed herein are embodiments of a Soft Bit Viterbi Equalizer (SBVE)based on an RSSE that produces soft bit values with relatively lessoverhead in terms of computational complexity. The SBVE is a variant ofthe Viterbi Algorithm that uses partially collapsed and completelycollapsed bidirectional cumulative metrics to improve the soft decisionperformance. Simulation results show a significant reduction in theoverall block error rate resulting from an improved accuracy of the softdecisions.

An implementation of the SBVE is presented for 8-PSK modulation due toits applicability in EDGE receivers. However, the SBVE can be used forany modulation scheme which can be partitioned based on an UngerboeckPartitioning Tree. For example, the SBVE can be adapted to modulationschemes such as QPSK or 16 QAM.

FIG. 1 is a block diagram of a baseband equivalent model of an EDGEtelecommunication system. The telecommunication system comprises atransmitter 10 that communicates with a receiver 12 over a communicationchannel 14. In one embodiment, the communication channel 14 comprises awireless channel modeled solely in the baseband domain by the TypicalUrban (TU) channel model as defined by the European TelecommunicationsStandards Institute (ETSI).

An information bit sequence 20 to be transmitted is processed by aconvolution, coding and puncturing component 22 of the transmitter 10.Using the convolution, coding and puncturing component 22, theinformation bit sequence 20 is coded using a rate ⅓ convolutionalencoder and punctured to achieve an overall coding rate of anappropriate modulation and coding scheme (MCS). A choice of MCS is madeby a Radio Link Control (RLC) at the transmitter 10 based on measurementfeedback from the receiver 12.

The resulting coded sequence is interleaved by an interleaving component24. The resulting coded and interleaved sequence is modulated by amodulator 26. In one embodiment, the modulator 26 comprises an 8-PSKmodulator that maps the coded and interleaved sequence to an 8-PSKconstellation based on the mapping shown in FIG. 2. The mapping is greycoded to achieve a reduced symbol error rate.

The resulting 8-PSK symbols are passed through a transmit filter 30before being transmitted. The transmit filter 30 is designed such thatthe 8-PSK signal has the same transmit spectral mask as the GMSK signal.As mentioned previously, the transmit filter 30 does not fulfillNyquist's ISI free sampling criteria and as a result introduces some ISIin the transmitted signal.

The transmitter 10 outputs the filtered signal to the communicationchannel 14. The filtered signal passes through a multipath,frequency-selective fading channel 32 which models the effect ofmultiple scattering in a wireless environment. For the purposes ofillustration and example, the channel 32 is modeled as a typical urban(TU) multipath channel to emulate a typical urban fading environment.Additive white Gaussian noise (AWGN) 34 is added to the signal to modelenvironmental noise in the communication channel 14 and/or noise in thereceiver 12.

The receiver 12 receives the signal via the communication channel 14.The receiver 12 includes a front-end filter 36 to process the signalfrom the communication channel 14. In one embodiment, the front-endfilter 36 comprises a root-raised cosine, low-pass filter with a 0.25roll-off. The filtered signal is sampled once every symbol to generatediscrete time samples thereof. The discrete time samples of the receivedsignal (post-front-end filter 36) can be related to the transmittedsignal (pre-transmit filter 30) and an overall channel impulse responseas $\begin{matrix}{x_{n} = {{\sum\limits_{l = 0}^{L}{h_{l}s_{n - l}}} + w_{n}}} & (2)\end{matrix}$where x represents the discrete time representation of the receivedsymbols (post-front-end filter 36), s represents the discrete timerepresentation of the transmitted symbols (pre-transmit filter 10), hrepresents the discrete time representation of the channel impulseresponse, and w represents the discrete time representation of the AWGNnoise 34.

The channel impulse response h includes the impulse response of thetransmit filter 30, the receive filter 36, and the multipath fadingchannel 14. The received signal (post-front-end filter 36) is passedthrough a pre-filter 40 that makes the overall impulse response of thesystem minimum phase. The transform of the channel impulse response H(z)can be represented in terms of its minimum phase equivalent and all-passequivalent asH(z)=H _(min)(z)H _(ap)(z)  (3)where H_(min) and H_(ap) are the minimum phase and all-pass equivalentsrespectively. The pre-filter 40 is directed by a channel estimationcomponent 42 to have an impulse response that is the inverse of H_(ap).This makes the overall channel response after the pre-filter 40 asH _(eff)(z)=H(z)H _(ap) ⁻¹(z)=H _(min)(z).  (4)

Since the partial energy of the minimum phase equivalent is highest, theeffective channel response is such that most of the energy is in theleading taps, which improves the performance of the RSSE.

In a MLSE, the state of the system is defined based on the K previoussymbols [x_(n−1), x_(n−2), . . . , x_(n−K)] where the number of statesis given by the number of possible modulation symbols raised to theK^(th) power. To reduce the number of states in an overall analysis ofan RSSE, each symbol of the modulation constellation is mapped ontonon-overlapping sets a_(i,k) where i indicates a set to which the symbolbelongs and k denotes a tap index. This two dimensional set partitioningallows for different set partitioning for different tap indices. Thus,in an RSSE, the state of the system is defined by the previous K sets[a_(n−1), a_(n−2), . . . , a_(n−K)].

Unlike an MLSE, an RSSE can have multiple, parallel transitions whichlead from one state to the next. While determining the survivingtrellis, at first, only the state transition with the minimum branchmetric is selected amongst the parallel transitions. Then amongstdifferent trellises, the trellis with the minimum cumulative metric isselected as the survivor coming into each state. Once the states havebeen defined in this manner, a traditional Viterbi Algorithm is appliedto estimate the most likely sequence.

As an example, FIG. 2 shows a possible set partitioning for 8-PSKmodulation. The eight symbols are partitioned into two non-overlappingsets. Thus, the number of the states in the system is reduced to 2^(K)in the RSSE compared to 8^(K) for the MLSE.

In the exemplary case of producing a minimum phase CIR, the pre-filter40 acts to minimize a symbol error rate in an RSSE. To achieve theminimum phase equivalent, the pre-filter 40 comprises a recursive filterwhich is the inverse of the all-pass component of the CIR as describedin equation (4). The overall CIR H(z), being FIR (i.e. having a finitenumber of roots), can be written as a product of two finite polynomials$\begin{matrix}{{H(z)} = {{{H_{1}(z)}{H_{2}(z)}} = {{H_{1}(z)}{H_{2}\left( z^{- 1} \right)}\frac{H_{2}(z)}{H_{2}\left( z^{- 1} \right)}}}} & (5)\end{matrix}$where H₁(z) has all the roots inside the unit circle and H₂(z) has allthe roots outside the unit circle. Based on this definition, the minimumphase and all-pass components are given by the following equations,respectively. $\begin{matrix}\begin{matrix}{{H_{\min}(z)} = {{H_{1}(z)}{H_{2}\left( z^{- 1} \right)}}} \\{{H_{ap}(z)} = \frac{H_{2}(z)}{H_{2}\left( z^{- 1} \right)}}\end{matrix} & (6)\end{matrix}$

An appropriate impulse response of the pre-filter 40 in this case wouldbe the inverse of the all-pass equivalent, which is given by:$\begin{matrix}{{H_{prefilter}(z)} = {\frac{H_{2}\left( z^{- 1} \right)}{H_{2}(z)}.}} & (7)\end{matrix}$

However, a causal implementation of the filter, which can be achieved bya recursive filter, is unstable since its poles are outside the unitcircle. This problem can be mitigated by viewing the pre-filter functionas non-causal, in which case the pre-filter 40 is stable. The receivedsignal is time-reversed and passed through the pre-filter 40 having aresponse of H_(prefiter)(1/z), which is non-causal but stable. This actresults in an output is given by:γ(z)=H _(prefilter)(1/z)X(1/z)   (8)where X represents the received signal before the pre-filter 40 and γ isthe non-causal output of the pre-filter 40. Performing anothertime-reversal of the output of the pre-filter 40 results in a causalrepresentation of the pre-filter output, Y, given by:Y(z)=γ(1/z)=H _(prefilter)(z)X(z).   (9)

From the perspective of the RSSE, the output of the pre-filter 40 can bewritten as: $\begin{matrix}{y_{n} = {{\sum\limits_{l = 0}^{L}{h_{l}^{\prime}s_{n - l}}} + v_{n}}} & (10)\end{matrix}$where h₁′ is equal to the convolution of h₁ with the impulse response ofthe pre-filter 40, h_(prefilter). Without loss of generality, h′ isreplaced by h hereinafter.

In a hard decision equalizer, the sequence of transmitted symbols isestimated such that the a-posteriori probability is maximized for thereceived sequence of symbols. Thus, the transmitted sequence isestimated to satisfy $\begin{matrix}{\max\limits_{\hat{s}}{P\left\{ {\left\lbrack {{\hat{s}}_{0},{\hat{s}}_{1},{...\quad{\hat{s}}_{N - 1}}} \right\rbrack ❘\left\lbrack {y_{0},y_{1},{...\quad y_{N - 1}}} \right\rbrack} \right\}}} & (11)\end{matrix}$where ŝ_(i) is an estimated transmit sequence and y_(i) is a receivedsequence. For a signal source with equally likely symbols, maximizingthe a-posteriori probability is equivalent to maximizing the likelihoodfunction, which is given by: $\begin{matrix}{{P\begin{Bmatrix}{\left\lbrack {y_{0},y_{1},{...\quad y_{N - 1}}} \right\rbrack ❘} \\\left\lbrack {{\hat{s}}_{0},{\hat{s}}_{1},{...\quad{\hat{s}}_{N - 1}}} \right\rbrack\end{Bmatrix}} = {\frac{1}{\sigma\sqrt{2\pi}}{\prod\limits_{n = 0}^{N - 1}\quad{\mathbb{e}}^{{- \frac{1}{2\sigma^{2}}}{({y_{n} - {\sum\limits_{l = 0}^{L}\quad{h_{l}{\hat{s}}_{n - 1}}}})}^{2}}}}} & (12)\end{matrix}$

The Viterbi Algorithm provides an efficient and optimum technique forestimating the transmitted sequence based on the maximization of thelikelihood function given in equation (12). If the memory order of thechannel is denoted by L, the effect of each symbol is persistent overthe current symbol and the next L symbols as seen at the receiver. Thusin order to estimate the likelihood ratio of a bit as defined byequation (1), the current and next L symbols are considered. Thisprocedure is repeated for each of the M bits that are used in creating asymbol. In the case of 8-PSK modulation, the estimation of thelikelihood ratio is performed for each of the three bits.

To simplify notation of the algorithm, the branch metric for the n^(th)transition between the states Ω_(n−1) and Ω_(n) is denoted as$\begin{matrix}{{\gamma\left( {n,\Omega_{n - 1},\Omega_{n},m} \right)} = \left( {y_{n} - {h_{0}e_{m}} - {\sum\limits_{l = 1}^{L}{h_{l}{\hat{s}}_{n - 1}}}} \right)^{2}} & (13)\end{matrix}$where m indicates a parallel transition index and e_(m) indicates asymbol corresponding to a parallel transition. Unlike the case of a harddecision equalizer, multiple branch metrics exist between the statesΩ_(n−1) and Ω_(n), one for each of the parallel transitions. Theprevious symbols for each trellis are denoted by ŝ_(n−1), and aredetermined by survivor processing per Viterbi Algorithm. The cumulativemetric for each of the states after the (n−1)^(th) transition is givenby, Γ(n−1, Ω_(n−1)), where Ω_(n−1) is the state index.

Two forward recursive partially collapsed metrics are defined as:$\begin{matrix}\begin{matrix}{{\Lambda^{+}\left( {n,\Omega_{n - 1},\Omega_{n - 1 + L}} \right)} = \begin{matrix}{{\Gamma\left( {{n - 1 + L},\Omega_{n - 1}} \right)} +} \\{\min\limits_{{\{{m_{i},\Omega_{n - 1 + i}}\}}_{+}}\left\lbrack {\sum\limits_{i = 0}^{L - 1}{\gamma\left( {{n + i},\Omega_{n - 1 + i},\Omega_{n + i},m_{i}} \right)}} \right\rbrack}\end{matrix}} \\{{\Lambda^{-}\left( {n,\Omega_{n - 1},\Omega_{n - 1 + L}} \right)} = \begin{matrix}{{\Gamma\left( {{n - 1 + L},\Omega_{n - 1}} \right)} +} \\{\min\limits_{{\{{m_{i},\Omega_{n - 1 + i}}\}}_{-}}{\left\lbrack {\sum\limits_{i = 0}^{L - 1}{\gamma\left( {{n + i},\Omega_{n - 1 + i},\Omega_{n + i},m_{i}} \right)}} \right\rbrack.}}\end{matrix}}\end{matrix} & (14)\end{matrix}$

The quantities Λ⁺ and Λ⁻¹ represent the cumulative metric of startingfrom state Ω_(n−1) and ending in state Ω_(n−1+L) in L transitions suchthat the n^(th) bit was +1 and −1 respectively. The minimum is evaluatedbetween the interim states Ω_(n−1+i) and the parallel transition indicesm_(i). For Λ⁺ only those m₀ which correspond to a symbol such that thebit=+1 are considered, and for Λ⁻ only those m₀ which correspond tosymbol such that the bit=−1 are considered. In the case of 8-PSKmodulation, this calculation is performed for each of the three bitssince the choices of m₀ for Λ⁺ and Λ⁻ are different for each of thethree bits. The minimum in equation (14) is jointly calculated over allthe possible transitions and parallel transitions from Ω_(n−1) toΩ_(n−1+L) in L symbol transitions.

Since the a-priori probability is given by the exponential of thecumulative metric, the probability of the bit corresponding to then^(th) transition being equal to +1 and −1 are given by the followingequations, respectively. $\begin{matrix}{{{p^{+}(n)} = {\sum\limits_{\Omega_{n - 1},\Omega_{n - 1 + L}}{\mathbb{e}}^{- {\Lambda^{+}{({n,\Omega_{n - 1},\Omega_{n - 1 + L}})}}}}}{{p^{-}(n)} = {\sum\limits_{\Omega_{n - 1},\Omega_{n - 1 + L}}{\mathbb{e}}^{- {\Lambda^{-}{({n,\Omega_{n - 1},\Omega_{n - 1 + L}})}}}}}} & (15)\end{matrix}$

The summation in (15) is over Ω_(n−1) to Ω_(n−1+L), which are theinternals states of the Viterbi algorithm before the (n−1)th and(n−1+L)th symbol transitions, respectively. For example, inimplementations having four possible states {0, 1, 2 and 3}, thesummation in (15) would be over 4×4 possible combinations {0,0}, {0,1},{0,2}, . . . {3,1}, {3,2} and {3,3}.

The soft log-likelihood ratio of the n^(th) bit is given by:$\begin{matrix}\begin{matrix}{{{LLR}(n)} = {\ln\quad\frac{p^{+}(n)}{p^{-}(n)}}} \\{= {{\ln\left\lbrack {\sum{\mathbb{e}}^{\lbrack{- {\Lambda^{+}{({n,\Omega_{n - 1},\Omega_{n - 1 + L}})}}}\rbrack}} \right\rbrack} -}} \\{{\ln\left\lbrack {\sum{\mathbb{e}}^{\lbrack{- {\Lambda^{-}{({n,\Omega_{n - 1},\Omega_{n - 1 + L}})}}}\rbrack}} \right\rbrack}.}\end{matrix} & (16)\end{matrix}$

Equations (15) and (16) are calculated separately for each of the bitsassociated with a given symbol. The following equationln(e ^(−x) +e ^(−y))=−min{x,y}+ln{1+e ^(−|y−x|)}  (17)provides an approximation of −min{x,y} if x<<y or y<<x. Equation (17)can be used to simplify the calculation of the a-priori probabilities.Using the approximation, the soft log-likelihood values for the n^(th)bit can be approximated by the following. $\begin{matrix}{{{LLR}(n)} = {{\min\limits_{\Omega_{n - 1},\Omega_{n - 1 + L}}\left\{ {\Lambda^{-}\left( {n,\Omega_{n - 1},\Omega_{n - 1 + L}} \right)} \right\}} - {\min\limits_{\Omega_{n - 1},\Omega_{n - 1 + L}}\left\{ {\Lambda^{+}\left( {n,\Omega_{n - 1},\Omega_{n - 1 + L}} \right)} \right\}}}} & (18)\end{matrix}$

After the soft log-likelihood value for the n^(th) symbol has beendetermined, the partially collapsed metrics Λ⁺ and Λ⁻ are collapsed togive the completely collapsed metric Γ. The relationship to do so can bedeveloped from the definition of the cumulative metric which is relatedto the a-priori probability of the system being in a particular stateafter a particular number of symbol transitions. $\begin{matrix}{\begin{matrix}{{\Pr\left\{ \Omega_{n} \right\}} = {\mathbb{e}}^{- {\Gamma{({n,\Omega_{n}})}}}} \\{= {{\sum\limits_{\Omega_{n - L}}{\mathbb{e}}^{\lbrack{- {\Lambda^{+}{({{n - L + 1},\Omega_{n - L},\Omega_{n}})}}}\rbrack}} + {\sum\limits_{\Omega_{n - L}}{\mathbb{e}}^{\lbrack{- {\Lambda^{-}{({{n - L + 1},\Omega_{n - L},\Omega_{n}})}}}\rbrack}}}}\end{matrix}{{\Gamma\left( {n,\Omega_{n}} \right)} = {- {\ln\left\lbrack {{\sum\limits_{\Omega_{n - L}}{\mathbb{e}}^{\lbrack{- {\Lambda^{+}{({{n - L + 1},\Omega_{n - L},\Omega_{n}})}}}\rbrack}} + {\sum\limits_{\Omega_{n - L}}{\mathbb{e}}^{\lbrack{- {\Lambda^{-}{({{n - L + 1},\Omega_{n - L},\Omega_{n}})}}}\rbrack}}} \right\rbrack}}}} & (19)\end{matrix}$

The approximation in equation (17) can be used to simplify equation (19)into the following form. $\begin{matrix}{{\Gamma\left( {n,\Omega_{n}} \right)} = {\min\left( {{\min\limits_{\Omega_{n - L}}\left( {\Lambda^{+}\left( {n,\Omega_{n - L},\Omega_{n}} \right)} \right)},{\min\limits_{\Omega_{n - L}}\left( {\Lambda^{-}\left( {n,\Omega_{n - L},\Omega_{n}} \right)} \right)}} \right)}} & (20)\end{matrix}$

The above-described process is iterated to calculate the soft likelihoodfor each of the symbols.

An SBVE receiver 44 determines the soft log-likelihood values based onthe output of the pre-filter 40 in the above-described way. Ade-interleaving component 46 de-interleaves the output of the SBVEreceiver 44. A Viterbi decoder 48 generates hard decisions based on thede-interleaved, soft log-likelihood values. The Viterbi decoder 48outputs a received information bit sequence 50 that ideally is the sameas the transmitted information bit sequence 20.

FIG. 3 is a flow chart of summarizing an embodiment of a method tocalculate the soft likelihood values by the SBVE receiver 44. The blocksin FIG. 3, which are illustrated for an n^(th) symbol transition, areperformed for each symbol transition.

As indicated by block 70, the method comprises calculating or otherwisedetermining a branch metric for all possible state transitions alongwith the parallel transitions γ(n, . . . ).

As indicated by block 72, the method comprises calculating or otherwisedetermining a first partially collapsed metric value Λ⁺(n, . . . ) foreach bit in an nth symbol transition. Each first partially collapsedmetric value is a cumulative metric of starting in a first state andending in a second state in L transitions with the respective bit in thenth symbol transition being a first value.

As indicated by block 74, the method comprises calculating or otherwisedetermining a second partially collapsed metric value Λ⁻(n, . . . ) foreach bit in an n^(th) symbol transition. Each second partially collapsedmetric value is a cumulative metric of starting in the first state andending in the second state in L transitions with the respective bit inthe n^(th) symbol transition being a second value. The second valuediffers from the first value (e.g. the second value may be −1 and thefirst value may be +1).

The acts indicated by blocks 72 and 74, which can be performed in anyorder, act to calculate partially collapsed metrics Λ⁺(n, . . . ) andΛ⁻(n, . . . ) based on the current and previous branch metrics and thecumulative metric Γ(n−L, . . . ).

As indicated by block 76, the method comprises calculating or otherwisedetermining a relative likelihood value, for each bit in the (n−L+1)thsymbol transition, based on its respective first partially collapsedmetric value and its respective second partially collapsed metric value.Each relative likelihood value may comprise a LLR, in which case the LLRfor the (n−L+1)th bit is calculated based on the partially collapsedmetrics Λ⁺(n−L+1, . . . ) and Λ⁻(n−L+1, . . . ). Thus, the LLRcalculation is not performed for the current symbol (i.e. the nthsymbol) but rather for the current-L+1 symbol due to channel lag. Inother words, the LLR computation lags the calculation of partial andcompletely collapsed metrics.

The acts indicated by blocks 72, 74 and 76 are repeated for all the bitsassociated with a symbol (3 for 8-PSK). This acts to separatelycalculate LLR values for each of the bits associated with a symboltransition.

As indicated by block 80, the method comprises calculating or otherwisedetermining another cumulative metric value based on the first andsecond partially collapsed metric values. The cumulative metric Γ(n−L+1,. . . ) is determined based on the partially collapsed metrics Λ⁺(n−L+1,. . . ) and Λ⁻(n−L+1, . . . ).

As indicated by block 82, the method comprises an act of performingsurvivor processing for the hard decisions for the (n−L+1)^(th)transition.

As indicated by block 84, the method comprises decoding a symbol basedon a hard decision performed using the relative likelihood values foreach bit in a symbol transition. With reference to FIG. 1, once the SBVEreceiver 44 has determined soft LLRs for all the bits, the Viterbidecoder 48 can make hard decisions based on the sign of the LLRs. Whencompared to a traditional Viterbi Algorithm, acts 72, 74 and 76 are theadditional processing performed by the SBVE receiver 44 to generate thesoft log-likelihood values.

Simulations were performed to quantify the performance benefit of theSBVE over symbol-by-symbol soft decoding. The simulations were run usingthe EDGE signal transmission format for 8-PSK with MCS7 (coding rate0.76). The transmitted signal is passed through a typical urban channelwith 3 km/hr mobile speed (TU3) at 1900 MHz to simulate the effect ofmultipath fading. A WGN noise is added to the faded signal to generatethe signal at the receiver. An initial CIR is estimated using thetraining sequence code (TSC) embedded within each GSM burst (one timeslot), which is used to calculate the response of the pre-filter 40. Thereceived signal is passed through the pre-filter 40 maximizing thepartial energies of the leading equalizer taps. The SBVE algorithm isused to obtain the soft log-likelihood based on the filtered signal. Thesign of the LLR is used to determine the channel bits (hard decision).The channel bits determined at the receiver 12 are compared with thechannel bits at the transmitter 10 to generate the channel or modem biterror rate (BER).

Soft log-likelihood values over four consecutive GSM bursts (1 RLCBlock=4 bursts) are used by the Viterbi decoder 48 to generate harddecisions of the original information bits. The estimated informationbits 50 are compared with the information bits 20 used by thetransmitter 10 to generate the block error rate (BLER).

FIG. 4 illustrates graphs of a simulated channel BER of a 4-state RSSEand a 512 state MLSE for 8-PSK modulation. The set partitioning chosenfor the 4-state RSSE is shown in FIG. 2, and the memory order of theequalizer is set to 2, which results in a total of 2² states within theequalizer. The 2-state RSSE uses the same set partitioning and has amemory order of 1.

The performance of the reduced state equalizers, particularly the4-state RSSE is remarkably close to the performance of the 512-stateMLSE. A difference exists in a range of 1 dB to 0.5 dB depending on thetargeted BER value. Since most systems are designed to achieve a channelBER of 10% to 5%, performance of the 4-state RSSE is acceptableconsidering that the amount of processing required is orders ofmagnitude less.

FIG. 5 illustrates graphs of simulated BLER performance of both the SBVEand a soft symbol decision RSSE. The soft symbol decision RSSE with thegiven set partitioning works much like a SDVE, where the likelihoodratio is defined as the ratio of the probabilities of the most likelysymbol belonging to either of the two sets. The most likely symbol ischosen from each of the two sets based on minimum metric, which providesthe hard decision. The sign of the LLR is determined by the harddecision, and the magnitude of the LLR is determined by the ratio of theprobabilities. Since all the three bits belonging to a single symbol areassigned the same magnitude of the LLR, this is in essencesymbol-by-symbol soft decoding.

The BLER is calculated for MCS7 using both of these equalizers and thedifference in performance is in the range of 1.5 dB to 2.5 dB dependingon the targeted BLER value. A difference of 2 dB translates to anincrease in the average timeslot throughput from 17.9 kbps to 27.7 kbpsfor an EDGE network deployed with 1/1 reuse and frequency hopping with20% fractional load. Thus the overall throughput and performance of thesystem increases by using the soft bit decoding as described hereincompared to a symbol-by-symbol soft decoding.

A new algorithm capable of bit-by-bit soft decoding of a 8-PSK signalfor EDGE has been introduced herein and characterized in terms of itsperformance. The algorithm allows an RSSE to develop reliable softlog-likelihood values on a bit-by-bit basis with relatively lesscomputational overhead. The algorithm enables the implementation of anEDGE receiver that is capable of multi-slot operation. Based onsimulation results, the performance of a receiver based on the algorithmis approximately 2 dB better than a receiver based on a symbol-by-symbolsoft decoding for MCS7. In a real implementation the performancedifference could be different depending on many factors including themodulation and coding scheme. Although presented in the framework of8-PSK modulation, the SBVE algorithm can be extended to other modulationschemes without loss of generality.

The herein-disclosed transmitter and receiver components and acts whichthey perform can be implemented in mobile radio telephones (e.g.cellular telephones) and/or mobile radio telephone base stations. Forexample, the herein-disclosed transmitter and receiver components andacts which they perform can be implemented by one or more integratedcircuits for mobile telephones (e.g. a mobile telephone chip set).

Acts performed by the herein-disclosed components can be directed byrespective computer program code embodied in a computer-readable form ona computer-readable medium. A computer processor responds to thecomputer program code to perform the acts.

It will be apparent to those skilled in the art that the disclosedembodiments may be modified in numerous ways and may assume manyembodiments other than the forms specifically set out and describedherein.

The above disclosed subject matter is to be considered illustrative, andnot restrictive, and the appended claims are intended to cover all suchmodifications, enhancements, and other embodiments which fall within thetrue spirit and scope of the present invention. Thus, to the maximumextent allowed by law, the scope of the present invention is to bedetermined by the broadest permissible interpretation of the followingclaims and their equivalents, and shall not be restricted or limited bythe foregoing detailed description.

1. A method of decoding data transmitted via a communication channel,the method comprising: determining a first partially collapsed metricvalue for each bit in a symbol transition, each first partiallycollapsed metric value being a cumulative metric of starting in a firststate and ending in a second state in L transitions with the respectivebit in the symbol transition being a first value, the first state andthe second state being internal states of a Viterbi algorithm;determining a second partially collapsed metric value for each bit inthe symbol transition, each second partially collapsed metric valuebeing a cumulative metric of starting in the first state and ending inthe second state in L transitions with the respective bit in the symboltransition being a second value, the second value differing from thefirst value; for each bit in the symbol transition, determining arelative likelihood value based on its respective first partiallycollapsed metric value and its respective second partially collapsedmetric value; and decoding at least one symbol based on a hard decisionperformed using the relative likelihood value for each bit in the symboltransition.
 2. The method of claim 1 wherein each relative likelihoodvalue is a log likelihood ratio based on its respective first partiallycollapsed metric value and its respective second partially collapsedmetric value.
 3. The method of claim 1 wherein determining the firstpartially collapsed metric value is based on a cumulative metric valueand a first minimum sum of branch metric values over all statetransitions and parallel transitions in L symbol transitions in whichthe respective bit in the symbol transition is the first value.
 4. Themethod of claim 3 wherein determining the second partially collapsedmetric value is based on the cumulative metric value and a secondminimum sum of branch metric values over all state transitions andparallel transitions in L symbol transitions in which the respective bitin the symbol transition is the second value.
 5. The method of claim 1further comprising: determining another cumulative metric value based onthe first and second partially collapsed metric values.
 6. A receiver todecode data transmitted via a communication channel, the receivercomprising: a soft bit equalizer to: determine a first partiallycollapsed metric value for each bit in an symbol transition, each firstpartially collapsed metric value being a cumulative metric of startingin a first state and ending in a second state in L transitions with therespective bit in the symbol transition being a first value, the firststate and the second state being internal states of a Viterbi algorithm;determine a second partially collapsed metric value for each bit in thesymbol transition, each second partially collapsed metric value being acumulative metric of starting in the first state and ending in thesecond state in L transitions with the respective bit in the symboltransition being a second value, the second value differing from thefirst value; and for each bit in the symbol transition, determine arelative likelihood value based on its respective first partiallycollapsed metric value and its respective second partially collapsedmetric value; and a decoder responsive to the soft bit equalizer, thedecoder to decode at least one symbol based on a hard decision performedusing the relative likelihood value for each bit in the symboltransition.
 7. The receiver of claim 6 wherein each relative likelihoodvalue is a log likelihood ratio based on its respective first partiallycollapsed metric value and its respective second partially collapsedmetric value.
 8. The receiver of claim 6 wherein the soft bit equalizeris to determine the first partially collapsed metric value based on acumulative metric value and a first minimum sum of branch metric valuesover all state transitions and parallel transitions in L symboltransitions in which the respective bit in the symbol transition is thefirst value.
 9. The receiver of claim 8 wherein the soft bit equalizeris to determine the second partially collapsed metric value based on thecumulative metric value and a second minimum sum of branch metric valuesover all state transitions and parallel transitions in L symboltransitions in which the respective bit in the symbol transition is thesecond value.
 10. The receiver of claim 6 further comprising:determining another cumulative metric value based on the first andsecond partially collapsed metric values.
 11. A computer-readable mediumhaving computer readable program code to cause a computer processor toperform acts comprising: determining a first partially collapsed metricvalue for each bit in an symbol transition, each first partiallycollapsed metric value being a cumulative metric of starting in a firststate and ending in a second state in L transitions with the respectivebit in the symbol transition being a first value, the first state andthe second state being internal states of a Viterbi algorithm;determining a second partially collapsed metric value for each bit inthe symbol transition, each second partially collapsed metric valuebeing a cumulative metric of starting in the first state and ending inthe second state in L transitions with the respective bit in the symboltransition being a second value, the second value differing from thefirst value; for each bit in the symbol transition, determining arelative likelihood value based on its respective first partiallycollapsed metric value and its respective second partially collapsedmetric value; and decoding at least one symbol based on a hard decisionperformed using the relative likelihood value for each bit in the symboltransition.
 12. The computer-readable medium of claim 11 wherein eachrelative likelihood value is a log likelihood ratio based on itsrespective first partially collapsed metric value and its respectivesecond partially collapsed metric value.
 13. The computer-readablemedium of claim 11 wherein determining the first partially collapsedmetric value is based on a cumulative metric value and a first minimumsum of branch metric values over all state transitions and paralleltransitions in L symbol transitions in which the respective bit in thesymbol transition is the first value.
 14. The computer-readable mediumof claim 13 wherein determining the second partially collapsed metricvalue is based on the cumulative metric value and a second minimum sumof branch metric values over all state transitions and paralleltransitions in L symbol transitions in which the respective bit in thesymbol transition is the second value.
 15. The computer-readable mediumof claim 11 wherein the acts further comprise: determining anothercumulative metric value based on the first and second partiallycollapsed metric values.